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Represent a periodic function with a Fourier series, determine their convergence, calculate even and odd series, and apply these to solving simple periodic systems

Perform change of variables for multivariable functions with the chain rule, use polar coordinates, represent 2D and 3D curves parametrically and solve line integrals on these curves

Manipulate and evaluate double and triple integrals in Cartesian, cylindrical and spherical coordinates

Calculate the gradient, divergence and curl vector operations, and apply these in the evaluation of surface and volume integrals through the Gauss and Stokes theorems

Solve elementary partial differential equations, apply boundary and initial conditions as appropriate, and use the method of separation of variables with the wave equation, heat equation and Laplace's equation

Appreciate key issues related to the numerical solution of full and sparse linear systems

Apply a range of suitable techniques for the numerical solution of ODEs, including using discrete Fourier transforms, PS and FE methods

Use a range of suitable simple numerical techniques for the solution of PDEs and appreciate their advantages and disadvantages

Use MATLAB and other appropriate software to assist in understanding these mathematical techniques

Express and explain mathematical techniques and arguments clearly in words.

Assessment

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Weekly assignments, quizzes or exercises: 40%

Examination (3 hours): 60%

Students are required to achieve at least 45% in the total continuous assessment component and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit.